I didn't say that a big chunk of China would get nuked. I used too few words to describe the idea that any military engagement in NK would almost certainly lead to damage to the bits of China on the border.

My point about 'they don't have to' was to illustrate that perception is super important. If they are perceived to have fast-response capable nukes, then they are going to be treated as if they do.

Soft infrastructure in all of Korea will get destroyed in the first couple hours with conventional weapons after that it will be a long painful slog. Even if you beat the north eventually the entirety of the south will lie in ruin.